Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3240,2,Mod(1,3240)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3240, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3240.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3240 = 2^{3} \cdot 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3240.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(25.8715302549\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{33}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.37228\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3240.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.37228 | −0.896638 | −0.448319 | − | 0.893874i | \(-0.647977\pi\) | ||||
−0.448319 | + | 0.893874i | \(0.647977\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.37228 | −1.01678 | −0.508391 | − | 0.861127i | \(-0.669759\pi\) | ||||
−0.508391 | + | 0.861127i | \(0.669759\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.37228 | 0.657952 | 0.328976 | − | 0.944338i | \(-0.393296\pi\) | ||||
0.328976 | + | 0.944338i | \(0.393296\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.74456 | 1.15073 | 0.575363 | − | 0.817898i | \(-0.304861\pi\) | ||||
0.575363 | + | 0.817898i | \(0.304861\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | 0.114708 | − | 0.993399i | \(-0.463407\pi\) | ||||
0.114708 | + | 0.993399i | \(0.463407\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.372281 | −0.0776260 | −0.0388130 | − | 0.999246i | \(-0.512358\pi\) | ||||
−0.0388130 | + | 0.999246i | \(0.512358\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.37228 | −0.626217 | −0.313108 | − | 0.949717i | \(-0.601370\pi\) | ||||
−0.313108 | + | 0.949717i | \(0.601370\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.11684 | −1.09862 | −0.549309 | − | 0.835619i | \(-0.685109\pi\) | ||||
−0.549309 | + | 0.835619i | \(0.685109\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.37228 | −0.400989 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.00000 | 0.986394 | 0.493197 | − | 0.869918i | \(-0.335828\pi\) | ||||
0.493197 | + | 0.869918i | \(0.335828\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11.7446 | 1.83419 | 0.917096 | − | 0.398666i | \(-0.130527\pi\) | ||||
0.917096 | + | 0.398666i | \(0.130527\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.74456 | 1.02854 | 0.514268 | − | 0.857629i | \(-0.328064\pi\) | ||||
0.514268 | + | 0.857629i | \(0.328064\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.62772 | −0.529157 | −0.264579 | − | 0.964364i | \(-0.585233\pi\) | ||||
−0.264579 | + | 0.964364i | \(0.585233\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.37228 | −0.196040 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.11684 | −0.977574 | −0.488787 | − | 0.872403i | \(-0.662560\pi\) | ||||
−0.488787 | + | 0.872403i | \(0.662560\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.37228 | −0.454718 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.00000 | 0.650945 | 0.325472 | − | 0.945552i | \(-0.394477\pi\) | ||||
0.325472 | + | 0.945552i | \(0.394477\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.25544 | 0.160742 | 0.0803711 | − | 0.996765i | \(-0.474389\pi\) | ||||
0.0803711 | + | 0.996765i | \(0.474389\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.37228 | 0.294245 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.7446 | 1.31266 | 0.656329 | − | 0.754475i | \(-0.272108\pi\) | ||||
0.656329 | + | 0.754475i | \(0.272108\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.37228 | 0.162860 | 0.0814299 | − | 0.996679i | \(-0.474051\pi\) | ||||
0.0814299 | + | 0.996679i | \(0.474051\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.25544 | 0.381020 | 0.190510 | − | 0.981685i | \(-0.438986\pi\) | ||||
0.190510 | + | 0.981685i | \(0.438986\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 8.00000 | 0.911685 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.74456 | 0.983840 | 0.491920 | − | 0.870640i | \(-0.336295\pi\) | ||||
0.491920 | + | 0.870640i | \(0.336295\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −10.0000 | −1.09764 | −0.548821 | − | 0.835940i | \(-0.684923\pi\) | ||||
−0.548821 | + | 0.835940i | \(0.684923\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.74456 | 0.514620 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.37228 | 0.145462 | 0.0727308 | − | 0.997352i | \(-0.476829\pi\) | ||||
0.0727308 | + | 0.997352i | \(0.476829\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.62772 | −0.589945 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.00000 | 0.102598 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.74456 | 0.684807 | 0.342403 | − | 0.939553i | \(-0.388759\pi\) | ||||
0.342403 | + | 0.939553i | \(0.388759\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.8614 | 1.27976 | 0.639879 | − | 0.768476i | \(-0.278985\pi\) | ||||
0.639879 | + | 0.768476i | \(0.278985\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 17.1168 | 1.68657 | 0.843286 | − | 0.537464i | \(-0.180618\pi\) | ||||
0.843286 | + | 0.537464i | \(0.180618\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.00000 | −0.580042 | −0.290021 | − | 0.957020i | \(-0.593662\pi\) | ||||
−0.290021 | + | 0.957020i | \(0.593662\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 18.1168 | 1.73528 | 0.867639 | − | 0.497194i | \(-0.165636\pi\) | ||||
0.867639 | + | 0.497194i | \(0.165636\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.25544 | 0.306246 | 0.153123 | − | 0.988207i | \(-0.451067\pi\) | ||||
0.153123 | + | 0.988207i | \(0.451067\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.372281 | −0.0347154 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −11.2554 | −1.03178 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.372281 | 0.0338438 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.8614 | 1.40747 | 0.703736 | − | 0.710461i | \(-0.251514\pi\) | ||||
0.703736 | + | 0.710461i | \(0.251514\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.7446 | 1.55035 | 0.775175 | − | 0.631747i | \(-0.217662\pi\) | ||||
0.775175 | + | 0.631747i | \(0.217662\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.37228 | −0.205703 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −16.7446 | −1.43058 | −0.715292 | − | 0.698825i | \(-0.753706\pi\) | ||||
−0.715292 | + | 0.698825i | \(0.753706\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.0000 | 1.27228 | 0.636142 | − | 0.771572i | \(-0.280529\pi\) | ||||
0.636142 | + | 0.771572i | \(0.280529\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −8.00000 | −0.668994 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.37228 | −0.280053 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.48913 | −0.285840 | −0.142920 | − | 0.989734i | \(-0.545649\pi\) | ||||
−0.142920 | + | 0.989734i | \(0.545649\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.6277 | 1.51590 | 0.757951 | − | 0.652311i | \(-0.226201\pi\) | ||||
0.757951 | + | 0.652311i | \(0.226201\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.11684 | −0.491317 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.86141 | −0.467791 | −0.233896 | − | 0.972262i | \(-0.575147\pi\) | ||||
−0.233896 | + | 0.972262i | \(0.575147\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.883156 | 0.0696024 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −13.4891 | −1.05655 | −0.528275 | − | 0.849073i | \(-0.677161\pi\) | ||||
−0.528275 | + | 0.849073i | \(0.677161\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −12.0000 | −0.928588 | −0.464294 | − | 0.885681i | \(-0.653692\pi\) | ||||
−0.464294 | + | 0.885681i | \(0.653692\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.37228 | −0.567099 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −13.8614 | −1.05386 | −0.526932 | − | 0.849908i | \(-0.676658\pi\) | ||||
−0.526932 | + | 0.849908i | \(0.676658\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.37228 | −0.179328 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −15.7446 | −1.17680 | −0.588402 | − | 0.808569i | \(-0.700243\pi\) | ||||
−0.588402 | + | 0.808569i | \(0.700243\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.8614 | 1.10464 | 0.552320 | − | 0.833632i | \(-0.313743\pi\) | ||||
0.552320 | + | 0.833632i | \(0.313743\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.00000 | 0.441129 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −16.0000 | −1.17004 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.3723 | −0.822869 | −0.411435 | − | 0.911439i | \(-0.634972\pi\) | ||||
−0.411435 | + | 0.911439i | \(0.634972\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.7446 | −0.773411 | −0.386705 | − | 0.922203i | \(-0.626387\pi\) | ||||
−0.386705 | + | 0.922203i | \(0.626387\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.37228 | −0.454006 | −0.227003 | − | 0.973894i | \(-0.572893\pi\) | ||||
−0.227003 | + | 0.973894i | \(0.572893\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.48913 | −0.672666 | −0.336333 | − | 0.941743i | \(-0.609187\pi\) | ||||
−0.336333 | + | 0.941743i | \(0.609187\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8.00000 | 0.561490 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.7446 | 0.820276 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.37228 | −0.233266 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.0000 | 1.17033 | 0.585164 | − | 0.810915i | \(-0.301030\pi\) | ||||
0.585164 | + | 0.810915i | \(0.301030\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.74456 | 0.459975 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 14.5109 | 0.985062 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 11.2554 | 0.757123 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.51087 | 0.168141 | 0.0840703 | − | 0.996460i | \(-0.473208\pi\) | ||||
0.0840703 | + | 0.996460i | \(0.473208\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.48913 | 0.364326 | 0.182163 | − | 0.983268i | \(-0.441690\pi\) | ||||
0.182163 | + | 0.983268i | \(0.441690\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.25544 | −0.347289 | −0.173645 | − | 0.984808i | \(-0.555554\pi\) | ||||
−0.173645 | + | 0.984808i | \(0.555554\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 20.2337 | 1.32555 | 0.662776 | − | 0.748817i | \(-0.269378\pi\) | ||||
0.662776 | + | 0.748817i | \(0.269378\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.62772 | −0.236646 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 14.2337 | 0.920701 | 0.460350 | − | 0.887737i | \(-0.347724\pi\) | ||||
0.460350 | + | 0.887737i | \(0.347724\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 29.6060 | 1.90709 | 0.953544 | − | 0.301254i | \(-0.0974051\pi\) | ||||
0.953544 | + | 0.301254i | \(0.0974051\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.37228 | −0.0876718 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.37228 | 0.150945 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 15.8614 | 1.00116 | 0.500582 | − | 0.865689i | \(-0.333120\pi\) | ||||
0.500582 | + | 0.865689i | \(0.333120\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.25544 | 0.0789287 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 23.4891 | 1.46521 | 0.732606 | − | 0.680653i | \(-0.238304\pi\) | ||||
0.732606 | + | 0.680653i | \(0.238304\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −14.2337 | −0.884438 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −13.1168 | −0.808819 | −0.404410 | − | 0.914578i | \(-0.632523\pi\) | ||||
−0.404410 | + | 0.914578i | \(0.632523\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.11684 | −0.437184 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 12.1168 | 0.738777 | 0.369389 | − | 0.929275i | \(-0.379567\pi\) | ||||
0.369389 | + | 0.929275i | \(0.379567\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −20.7446 | −1.26014 | −0.630071 | − | 0.776537i | \(-0.716974\pi\) | ||||
−0.630071 | + | 0.776537i | \(0.716974\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.37228 | −0.203356 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −17.1168 | −1.02845 | −0.514226 | − | 0.857655i | \(-0.671921\pi\) | ||||
−0.514226 | + | 0.857655i | \(0.671921\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 11.6277 | 0.693652 | 0.346826 | − | 0.937930i | \(-0.387260\pi\) | ||||
0.346826 | + | 0.937930i | \(0.387260\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.25544 | 0.312403 | 0.156202 | − | 0.987725i | \(-0.450075\pi\) | ||||
0.156202 | + | 0.987725i | \(0.450075\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −27.8614 | −1.64461 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.51087 | 0.324169 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 13.8614 | 0.809792 | 0.404896 | − | 0.914363i | \(-0.367308\pi\) | ||||
0.404896 | + | 0.914363i | \(0.367308\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.00000 | 0.291111 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.883156 | −0.0510742 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −16.0000 | −0.922225 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.25544 | 0.0718861 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10.7446 | −0.613225 | −0.306612 | − | 0.951834i | \(-0.599195\pi\) | ||||
−0.306612 | + | 0.951834i | \(0.599195\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.8614 | −0.615894 | −0.307947 | − | 0.951404i | \(-0.599642\pi\) | ||||
−0.307947 | + | 0.951404i | \(0.599642\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.00000 | −0.226093 | −0.113047 | − | 0.993590i | \(-0.536061\pi\) | ||||
−0.113047 | + | 0.993590i | \(0.536061\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −16.3723 | −0.919559 | −0.459779 | − | 0.888033i | \(-0.652072\pi\) | ||||
−0.459779 | + | 0.888033i | \(0.652072\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 11.3723 | 0.636726 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.74456 | 0.263995 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.37228 | 0.131590 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.60597 | 0.474462 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.3723 | 1.06480 | 0.532398 | − | 0.846494i | \(-0.321291\pi\) | ||||
0.532398 | + | 0.846494i | \(0.321291\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 10.7446 | 0.587038 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.744563 | 0.0405589 | 0.0202795 | − | 0.999794i | \(-0.493544\pi\) | ||||
0.0202795 | + | 0.999794i | \(0.493544\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 20.6277 | 1.11705 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.8614 | 1.07242 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −30.2337 | −1.62303 | −0.811515 | − | 0.584332i | \(-0.801357\pi\) | ||||
−0.811515 | + | 0.584332i | \(0.801357\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −25.3723 | −1.35815 | −0.679074 | − | 0.734070i | \(-0.737618\pi\) | ||||
−0.679074 | + | 0.734070i | \(0.737618\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 24.9783 | 1.32946 | 0.664729 | − | 0.747085i | \(-0.268547\pi\) | ||||
0.664729 | + | 0.747085i | \(0.268547\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.37228 | 0.0728331 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −10.6277 | −0.560910 | −0.280455 | − | 0.959867i | \(-0.590485\pi\) | ||||
−0.280455 | + | 0.959867i | \(0.590485\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.0000 | −0.947368 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.25544 | 0.170397 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.23369 | 0.220997 | 0.110498 | − | 0.993876i | \(-0.464755\pi\) | ||||
0.110498 | + | 0.993876i | \(0.464755\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 16.8832 | 0.876530 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.744563 | 0.0385520 | 0.0192760 | − | 0.999814i | \(-0.493864\pi\) | ||||
0.0192760 | + | 0.999814i | \(0.493864\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −8.00000 | −0.412021 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 25.3505 | 1.30217 | 0.651085 | − | 0.759005i | \(-0.274314\pi\) | ||||
0.651085 | + | 0.759005i | \(0.274314\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −13.6277 | −0.696344 | −0.348172 | − | 0.937431i | \(-0.613197\pi\) | ||||
−0.348172 | + | 0.937431i | \(0.613197\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.00000 | 0.407718 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9.25544 | 0.469269 | 0.234635 | − | 0.972084i | \(-0.424611\pi\) | ||||
0.234635 | + | 0.972084i | \(0.424611\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.76631 | −0.0893262 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8.74456 | 0.439987 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 34.0000 | 1.70641 | 0.853206 | − | 0.521575i | \(-0.174655\pi\) | ||||
0.853206 | + | 0.521575i | \(0.174655\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15.3505 | −0.766569 | −0.383284 | − | 0.923630i | \(-0.625207\pi\) | ||||
−0.383284 | + | 0.923630i | \(0.625207\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −14.5109 | −0.722838 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −20.2337 | −1.00295 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −15.6277 | −0.772741 | −0.386370 | − | 0.922344i | \(-0.626271\pi\) | ||||
−0.386370 | + | 0.922344i | \(0.626271\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −11.8614 | −0.583662 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −10.0000 | −0.490881 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10.9783 | −0.536323 | −0.268161 | − | 0.963374i | \(-0.586416\pi\) | ||||
−0.268161 | + | 0.963374i | \(0.586416\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.6277 | 1.10281 | 0.551404 | − | 0.834239i | \(-0.314092\pi\) | ||||
0.551404 | + | 0.834239i | \(0.314092\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.74456 | 0.230145 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.97825 | −0.144128 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15.3723 | 0.740457 | 0.370228 | − | 0.928941i | \(-0.379279\pi\) | ||||
0.370228 | + | 0.928941i | \(0.379279\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 39.2119 | 1.88441 | 0.942203 | − | 0.335043i | \(-0.108751\pi\) | ||||
0.942203 | + | 0.335043i | \(0.108751\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.372281 | −0.0178086 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 31.0951 | 1.48409 | 0.742044 | − | 0.670351i | \(-0.233857\pi\) | ||||
0.742044 | + | 0.670351i | \(0.233857\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16.9783 | 0.806661 | 0.403331 | − | 0.915054i | \(-0.367852\pi\) | ||||
0.403331 | + | 0.915054i | \(0.367852\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.37228 | 0.0650524 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −22.7228 | −1.07236 | −0.536178 | − | 0.844105i | \(-0.680132\pi\) | ||||
−0.536178 | + | 0.844105i | \(0.680132\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −39.6060 | −1.86497 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5.62772 | −0.263832 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −40.2337 | −1.88205 | −0.941026 | − | 0.338334i | \(-0.890137\pi\) | ||||
−0.941026 | + | 0.338334i | \(0.890137\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.8832 | 0.646603 | 0.323302 | − | 0.946296i | \(-0.395207\pi\) | ||||
0.323302 | + | 0.946296i | \(0.395207\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −21.8614 | −1.01599 | −0.507993 | − | 0.861361i | \(-0.669612\pi\) | ||||
−0.507993 | + | 0.861361i | \(0.669612\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −18.2337 | −0.843754 | −0.421877 | − | 0.906653i | \(-0.638629\pi\) | ||||
−0.421877 | + | 0.906653i | \(0.638629\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −25.4891 | −1.17698 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −22.7446 | −1.04580 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.00000 | 0.0458831 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −24.1168 | −1.10193 | −0.550963 | − | 0.834529i | \(-0.685740\pi\) | ||||
−0.550963 | + | 0.834529i | \(0.685740\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 14.2337 | 0.649000 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6.74456 | 0.306255 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −20.6060 | −0.933746 | −0.466873 | − | 0.884324i | \(-0.654619\pi\) | ||||
−0.466873 | + | 0.884324i | \(0.654619\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 19.9783 | 0.901606 | 0.450803 | − | 0.892624i | \(-0.351138\pi\) | ||||
0.450803 | + | 0.892624i | \(0.351138\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −16.0000 | −0.720604 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.25544 | −0.146026 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.25544 | 0.369564 | 0.184782 | − | 0.982780i | \(-0.440842\pi\) | ||||
0.184782 | + | 0.982780i | \(0.440842\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −34.9783 | −1.55960 | −0.779802 | − | 0.626027i | \(-0.784680\pi\) | ||||
−0.779802 | + | 0.626027i | \(0.784680\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.8614 | 0.572325 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −38.0000 | −1.68432 | −0.842160 | − | 0.539227i | \(-0.818716\pi\) | ||||
−0.842160 | + | 0.539227i | \(0.818716\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.72281 | −0.341637 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 17.1168 | 0.754258 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12.2337 | 0.538037 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17.1168 | 0.749903 | 0.374951 | − | 0.927045i | \(-0.377659\pi\) | ||||
0.374951 | + | 0.927045i | \(0.377659\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.76631 | −0.252143 | −0.126072 | − | 0.992021i | \(-0.540237\pi\) | ||||
−0.126072 | + | 0.992021i | \(0.540237\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −29.0217 | −1.26421 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.8614 | −0.993974 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 27.8614 | 1.20681 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.00000 | −0.259403 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.62772 | 0.199330 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −38.3505 | −1.64882 | −0.824409 | − | 0.565994i | \(-0.808492\pi\) | ||||
−0.824409 | + | 0.565994i | \(0.808492\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 18.1168 | 0.776040 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −40.0000 | −1.71028 | −0.855138 | − | 0.518400i | \(-0.826528\pi\) | ||||
−0.855138 | + | 0.518400i | \(0.826528\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.37228 | −0.143664 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −20.7446 | −0.882149 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 8.60597 | 0.364647 | 0.182323 | − | 0.983239i | \(-0.441638\pi\) | ||||
0.182323 | + | 0.983239i | \(0.441638\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 16.0000 | 0.676728 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 24.2337 | 1.02133 | 0.510664 | − | 0.859780i | \(-0.329400\pi\) | ||||
0.510664 | + | 0.859780i | \(0.329400\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.25544 | 0.136957 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 43.2337 | 1.81245 | 0.906225 | − | 0.422795i | \(-0.138951\pi\) | ||||
0.906225 | + | 0.422795i | \(0.138951\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.1168 | 0.590772 | 0.295386 | − | 0.955378i | \(-0.404552\pi\) | ||||
0.295386 | + | 0.955378i | \(0.404552\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.372281 | −0.0155252 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 13.4891 | 0.561560 | 0.280780 | − | 0.959772i | \(-0.409407\pi\) | ||||
0.280780 | + | 0.959772i | \(0.409407\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 23.7228 | 0.984188 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 24.0000 | 0.993978 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 30.0000 | 1.23823 | 0.619116 | − | 0.785299i | \(-0.287491\pi\) | ||||
0.619116 | + | 0.785299i | \(0.287491\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.11684 | −0.252040 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 16.9783 | 0.697213 | 0.348607 | − | 0.937269i | \(-0.386655\pi\) | ||||
0.348607 | + | 0.937269i | \(0.386655\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −11.2554 | −0.461428 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −36.3505 | −1.48524 | −0.742621 | − | 0.669712i | \(-0.766418\pi\) | ||||
−0.742621 | + | 0.669712i | \(0.766418\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 13.0000 | 0.530281 | 0.265141 | − | 0.964210i | \(-0.414582\pi\) | ||||
0.265141 | + | 0.964210i | \(0.414582\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.372281 | 0.0151354 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −33.2554 | −1.34980 | −0.674898 | − | 0.737911i | \(-0.735813\pi\) | ||||
−0.674898 | + | 0.737911i | \(0.735813\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8.60597 | −0.348160 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −33.3505 | −1.34702 | −0.673508 | − | 0.739180i | \(-0.735213\pi\) | ||||
−0.673508 | + | 0.739180i | \(0.735213\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −43.7228 | −1.76021 | −0.880107 | − | 0.474775i | \(-0.842529\pi\) | ||||
−0.880107 | + | 0.474775i | \(0.842529\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −38.3723 | −1.54231 | −0.771156 | − | 0.636646i | \(-0.780321\pi\) | ||||
−0.771156 | + | 0.636646i | \(0.780321\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.25544 | −0.130426 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 28.4674 | 1.13507 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −36.6277 | −1.45813 | −0.729063 | − | 0.684446i | \(-0.760044\pi\) | ||||
−0.729063 | + | 0.684446i | \(0.760044\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 15.8614 | 0.629441 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.25544 | −0.128985 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.39403 | 0.0945585 | 0.0472793 | − | 0.998882i | \(-0.484945\pi\) | ||||
0.0472793 | + | 0.998882i | \(0.484945\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21.2554 | 0.838233 | 0.419116 | − | 0.907933i | \(-0.362340\pi\) | ||||
0.419116 | + | 0.907933i | \(0.362340\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 25.7228 | 1.01127 | 0.505634 | − | 0.862748i | \(-0.331259\pi\) | ||||
0.505634 | + | 0.862748i | \(0.331259\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −16.8614 | −0.661868 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −24.7446 | −0.968330 | −0.484165 | − | 0.874977i | \(-0.660876\pi\) | ||||
−0.484165 | + | 0.874977i | \(0.660876\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 17.7446 | 0.693337 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −47.5842 | −1.85362 | −0.926809 | − | 0.375533i | \(-0.877460\pi\) | ||||
−0.926809 | + | 0.375533i | \(0.877460\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −45.0951 | −1.75400 | −0.876998 | − | 0.480494i | \(-0.840457\pi\) | ||||
−0.876998 | + | 0.480494i | \(0.840457\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.37228 | −0.0919931 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.25544 | 0.0486107 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.23369 | −0.163440 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.510875 | −0.0196928 | −0.00984639 | − | 0.999952i | \(-0.503134\pi\) | ||||
−0.00984639 | + | 0.999952i | \(0.503134\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −21.1168 | −0.811586 | −0.405793 | − | 0.913965i | \(-0.633005\pi\) | ||||
−0.405793 | + | 0.913965i | \(0.633005\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −16.0000 | −0.614024 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 38.2337 | 1.46297 | 0.731486 | − | 0.681857i | \(-0.238827\pi\) | ||||
0.731486 | + | 0.681857i | \(0.238827\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −16.7446 | −0.639777 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −16.8832 | −0.643197 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 41.3505 | 1.57305 | 0.786524 | − | 0.617559i | \(-0.211879\pi\) | ||||
0.786524 | + | 0.617559i | \(0.211879\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 15.0000 | 0.568982 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 55.7228 | 2.11065 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.11684 | −0.306569 | −0.153284 | − | 0.988182i | \(-0.548985\pi\) | ||||
−0.153284 | + | 0.988182i | \(0.548985\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.00000 | 0.226294 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −30.5109 | −1.14748 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 18.4674 | 0.693557 | 0.346778 | − | 0.937947i | \(-0.387276\pi\) | ||||
0.346778 | + | 0.937947i | \(0.387276\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.27719 | 0.0852813 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8.00000 | −0.299183 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −10.3940 | −0.387632 | −0.193816 | − | 0.981038i | \(-0.562086\pi\) | ||||
−0.193816 | + | 0.981038i | \(0.562086\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −40.6060 | −1.51225 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.37228 | −0.125243 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −47.1168 | −1.74747 | −0.873734 | − | 0.486405i | \(-0.838308\pi\) | ||||
−0.873734 | + | 0.486405i | \(0.838308\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 32.0000 | 1.18356 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −28.9783 | −1.07034 | −0.535168 | − | 0.844746i | \(-0.679752\pi\) | ||||
−0.535168 | + | 0.844746i | \(0.679752\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −36.2337 | −1.33469 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −12.8614 | −0.473114 | −0.236557 | − | 0.971618i | \(-0.576019\pi\) | ||||
−0.236557 | + | 0.971618i | \(0.576019\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −29.4891 | −1.08185 | −0.540926 | − | 0.841070i | \(-0.681926\pi\) | ||||
−0.540926 | + | 0.841070i | \(0.681926\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.48913 | −0.127832 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 14.2337 | 0.520088 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −38.2337 | −1.39517 | −0.697584 | − | 0.716503i | \(-0.745741\pi\) | ||||
−0.697584 | + | 0.716503i | \(0.745741\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 18.6277 | 0.677932 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 27.1168 | 0.985578 | 0.492789 | − | 0.870149i | \(-0.335977\pi\) | ||||
0.492789 | + | 0.870149i | \(0.335977\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −17.2337 | −0.624721 | −0.312360 | − | 0.949964i | \(-0.601120\pi\) | ||||
−0.312360 | + | 0.949964i | \(0.601120\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −42.9783 | −1.55592 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 11.8614 | 0.428291 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −32.3505 | −1.16659 | −0.583295 | − | 0.812260i | \(-0.698237\pi\) | ||||
−0.583295 | + | 0.812260i | \(0.698237\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 18.0000 | 0.647415 | 0.323708 | − | 0.946157i | \(-0.395071\pi\) | ||||
0.323708 | + | 0.946157i | \(0.395071\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.11684 | −0.219724 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 11.7446 | 0.420793 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.62772 | −0.165593 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.86141 | −0.209203 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15.7228 | 0.560458 | 0.280229 | − | 0.959933i | \(-0.409590\pi\) | ||||
0.280229 | + | 0.959933i | \(0.409590\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −7.72281 | −0.274592 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.97825 | 0.105761 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 14.2337 | 0.504183 | 0.252092 | − | 0.967703i | \(-0.418882\pi\) | ||||
0.252092 | + | 0.967703i | \(0.418882\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −17.2119 | −0.608915 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −10.9783 | −0.387414 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.883156 | 0.0311272 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −34.2119 | −1.20283 | −0.601414 | − | 0.798938i | \(-0.705396\pi\) | ||||
−0.601414 | + | 0.798938i | \(0.705396\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 14.3505 | 0.503915 | 0.251958 | − | 0.967738i | \(-0.418926\pi\) | ||||
0.251958 | + | 0.967738i | \(0.418926\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −13.4891 | −0.472503 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.74456 | 0.235962 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 41.3723 | 1.44390 | 0.721951 | − | 0.691944i | \(-0.243245\pi\) | ||||
0.721951 | + | 0.691944i | \(0.243245\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −34.7446 | −1.21112 | −0.605560 | − | 0.795800i | \(-0.707051\pi\) | ||||
−0.605560 | + | 0.795800i | \(0.707051\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 45.9565 | 1.59806 | 0.799032 | − | 0.601288i | \(-0.205346\pi\) | ||||
0.799032 | + | 0.601288i | \(0.205346\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 42.5842 | 1.47901 | 0.739506 | − | 0.673150i | \(-0.235059\pi\) | ||||
0.739506 | + | 0.673150i | \(0.235059\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.51087 | −0.225588 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −12.0000 | −0.415277 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 11.6060 | 0.400683 | 0.200341 | − | 0.979726i | \(-0.435795\pi\) | ||||
0.200341 | + | 0.979726i | \(0.435795\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17.6277 | −0.607852 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −7.37228 | −0.253614 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.883156 | −0.0303456 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.23369 | −0.0765698 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −0.744563 | −0.0254933 | −0.0127467 | − | 0.999919i | \(-0.504058\pi\) | ||||
−0.0127467 | + | 0.999919i | \(0.504058\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −44.7446 | −1.52845 | −0.764223 | − | 0.644953i | \(-0.776877\pi\) | ||||
−0.764223 | + | 0.644953i | \(0.776877\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 50.3505 | 1.71794 | 0.858969 | − | 0.512028i | \(-0.171105\pi\) | ||||
0.858969 | + | 0.512028i | \(0.171105\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −11.3940 | −0.387857 | −0.193929 | − | 0.981016i | \(-0.562123\pi\) | ||||
−0.193929 | + | 0.981016i | \(0.562123\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −13.8614 | −0.471302 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −29.4891 | −1.00035 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 25.4891 | 0.863666 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.37228 | −0.0801977 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8.88316 | 0.299963 | 0.149981 | − | 0.988689i | \(-0.452079\pi\) | ||||
0.149981 | + | 0.988689i | \(0.452079\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 25.3723 | 0.854814 | 0.427407 | − | 0.904059i | \(-0.359427\pi\) | ||||
0.427407 | + | 0.904059i | \(0.359427\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.76631 | 0.194052 | 0.0970259 | − | 0.995282i | \(-0.469067\pi\) | ||||
0.0970259 | + | 0.995282i | \(0.469067\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −41.8614 | −1.40557 | −0.702784 | − | 0.711403i | \(-0.748060\pi\) | ||||
−0.702784 | + | 0.711403i | \(0.748060\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −37.6277 | −1.26199 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.62772 | −0.121397 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −15.7446 | −0.526283 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 20.6277 | 0.687973 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −33.7663 | −1.12492 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 14.8614 | 0.494010 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −35.4891 | −1.17840 | −0.589199 | − | 0.807988i | \(-0.700556\pi\) | ||||
−0.589199 | + | 0.807988i | \(0.700556\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 54.0733 | 1.79153 | 0.895765 | − | 0.444528i | \(-0.146629\pi\) | ||||
0.895765 | + | 0.444528i | \(0.146629\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 33.7228 | 1.11606 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −42.0951 | −1.39010 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 42.1168 | 1.38931 | 0.694653 | − | 0.719345i | \(-0.255558\pi\) | ||||
0.694653 | + | 0.719345i | \(0.255558\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.25544 | 0.107154 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.00000 | 0.197279 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.86141 | −0.0938797 | −0.0469399 | − | 0.998898i | \(-0.514947\pi\) | ||||
−0.0469399 | + | 0.998898i | \(0.514947\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.37228 | −0.0449747 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −16.0000 | −0.523256 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 42.7446 | 1.39640 | 0.698202 | − | 0.715901i | \(-0.253984\pi\) | ||||
0.698202 | + | 0.715901i | \(0.253984\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 26.4674 | 0.862812 | 0.431406 | − | 0.902158i | \(-0.358018\pi\) | ||||
0.431406 | + | 0.902158i | \(0.358018\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.37228 | −0.142381 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 37.2554 | 1.21064 | 0.605320 | − | 0.795983i | \(-0.293045\pi\) | ||||
0.605320 | + | 0.795983i | \(0.293045\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.72281 | 0.250693 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −12.0000 | −0.388718 | −0.194359 | − | 0.980930i | \(-0.562263\pi\) | ||||
−0.194359 | + | 0.980930i | \(0.562263\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −11.3723 | −0.367998 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 39.7228 | 1.28272 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.41578 | 0.206961 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −10.7446 | −0.345880 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −18.5109 | −0.595270 | −0.297635 | − | 0.954680i | \(-0.596198\pi\) | ||||
−0.297635 | + | 0.954680i | \(0.596198\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −8.72281 | −0.279928 | −0.139964 | − | 0.990157i | \(-0.544699\pi\) | ||||
−0.139964 | + | 0.990157i | \(0.544699\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −35.5842 | −1.14078 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 17.7663 | 0.568395 | 0.284197 | − | 0.958766i | \(-0.408273\pi\) | ||||
0.284197 | + | 0.958766i | \(0.408273\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.62772 | −0.147903 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −5.48913 | −0.175076 | −0.0875380 | − | 0.996161i | \(-0.527900\pi\) | ||||
−0.0875380 | + | 0.996161i | \(0.527900\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.37228 | −0.203038 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.51087 | −0.0798412 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.37228 | 0.107124 | 0.0535620 | − | 0.998565i | \(-0.482943\pi\) | ||||
0.0535620 | + | 0.998565i | \(0.482943\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −9.48913 | −0.300825 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9.35053 | 0.296134 | 0.148067 | − | 0.988977i | \(-0.452695\pi\) | ||||
0.148067 | + | 0.988977i | \(0.452695\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 3240.2.a.m.1.1 | yes | 2 | |
3.2 | odd | 2 | 3240.2.a.i.1.1 | ✓ | 2 | ||
4.3 | odd | 2 | 6480.2.a.bo.1.2 | 2 | |||
9.2 | odd | 6 | 3240.2.q.bd.1081.2 | 4 | |||
9.4 | even | 3 | 3240.2.q.ba.2161.2 | 4 | |||
9.5 | odd | 6 | 3240.2.q.bd.2161.2 | 4 | |||
9.7 | even | 3 | 3240.2.q.ba.1081.2 | 4 | |||
12.11 | even | 2 | 6480.2.a.bd.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3240.2.a.i.1.1 | ✓ | 2 | 3.2 | odd | 2 | ||
3240.2.a.m.1.1 | yes | 2 | 1.1 | even | 1 | trivial | |
3240.2.q.ba.1081.2 | 4 | 9.7 | even | 3 | |||
3240.2.q.ba.2161.2 | 4 | 9.4 | even | 3 | |||
3240.2.q.bd.1081.2 | 4 | 9.2 | odd | 6 | |||
3240.2.q.bd.2161.2 | 4 | 9.5 | odd | 6 | |||
6480.2.a.bd.1.2 | 2 | 12.11 | even | 2 | |||
6480.2.a.bo.1.2 | 2 | 4.3 | odd | 2 |